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Re: [Phys-l] quadratic uncertainty



One possibility is to use the Monte Carlo method. Suppose the distribution of uncertainties (in a, b and c) are gaussian.

a) Select a, b, c by using a random number generator. Then solve for x
b) Repeat this 1000 times, for example, and plot the resulting distribution of x

But for any given of (a,b,c) we have two solutions for x. I am not sure how to deal with this. Is selecting + or - randomly acceptable? I have to think about this.

Ludwik Kowalski




On Aug 25, 2010, at 11:09 PM, John Denker wrote:

Here's a little puzzle with some seasonal relevance:

We need to find a good value for x
/and for the uncertainty associated with x/
given that:
a x^2 + b x + c = 0 [1]
a = 1 ± .0001
b = -2.08 ± .01
c = 1.08 ± .01

This was mentioned in connection with the annual "sig figs"
donnybrook on the chemistry list. There are a thousand people
on that list, and so far nobody has come up with a solution.
One person came kinda close, but no cigar.

I think it's safe to say that the problem is more interesting
than it might at first appear. The interest-to-difficulty
ratio is pretty good IMHO. After all, it's just a quadratic,
so there's a limit to how hard it can be.

The point of the exercise is to propagate the uncertainty
from the inputs (a,b,c) to the result (x). A lot of people
talk the talk about propagation of uncertainty but have not
much experience actually walking the walk, especially when
it comes to calculations that require more than two or three
steps.

Any method of solution you can think of is fair game.

So ... any takers?

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Ludwik

http://csam.montclair.edu/~kowalski/life/intro.html